Combinatorial Yamabe flow on hyperbolic surfaces with boundary

Ren Guo

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arXiv · 1003.3910

Combinatorial Yamabe flow on hyperbolic surfaces with boundary

Ren Guo

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Abstract

This paper studies the combinatorial Yamabe flow on hyperbolic surfaces with boundary. It is proved by applying a variational principle that the length of boundary components is uniquely determined by the combinatorial conformal factor. The combinatorial Yamabe flow is a gradient flow of a concave function. The long time behavior of the flow and the geometric meaning is investigated.

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Ren Guo. 2010-03-20. Combinatorial Yamabe flow on hyperbolic surfaces with boundary. https://arxiv.org/abs/1003.3910

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